There’s a tendency, in 2016, to think of the Flaming Lips as rather soft-bellied beasts – glitter cannons, confetti explosions and laser-shooting hands. They’ve struggled in recent times to produce anything more striking than some by-the-numbers wackiness with Miley Cyrus. At their very best, though, Oklahoma’s finest have produced wonderful and strange pop music that, for all its oddness, is littered with sublime little truths. Witness the sweet spot they hit on this ramshackle alt-country stomp, from 1990’s In a Priest Driven Ambulance. “I was born the day they shot JFK / The way you look at me sucks me down the sidewalk / Somebody please tell this machine I’m not a machine,” babbles frontman Wayne Coyne, before suddenly turning into a psych-rock savant who’s stumbled upon some deep, dark secret. “You’re fucked if you do, and you’re fucked if you don’t,” he howls. He would later explain the Flaming Lips ethos: “We wanted to sing about shit that we truly didn’t understand, but then we would come up with these lines that cut right to the heart of things.” That was their essence: to find pockets of meaning in the most peculiar places.

The Flaming Lips were always blessed with the type of origin story that could have been lifted from a comic book – it’s easy to imagine flipping through the pages of The Adventures of Young Wayne Coyne, the tale of a normal kid from Oklahoma whose life was turned upside down when he spied some musical instruments in a church hall and, on a whim, decided to pinch them and start a band. But it took some time before the music lived up to the creation myth. The band’s first studio three albums were patchy, their line-up was constantly chopping and changing, and they had to wait seven years and four records for their first great LP, In a Priest Driven Ambulance, to arrive. By 1992’s major label debut Hit to Death in the Future Head, though, Coyne and his bandmates – including Mercury Rev guitarist Jonathan Donahue – had learnt to marry the odd flights of fancy with canny pop nous. The Sun, in particular, is a splendid little thing, with its wicked, misshapen strings bending this way and that as guitars bloom and burst. “It’d be so kind to see your face in my door,” sings Coyne sweetly, and even though it’s a line stolen from Carole King’s So Far Away, it’s used to make something entirely their own.

She Don’t Use Jelly didn’t do for the Flaming Lips what Smells Like Teen Spirit did for Nirvana, or Creep did for Radiohead, but it came close: in 1993 it became their biggest hit and an unlikely success, eventually peaking at a career-high No 9 in the Billboard chart, and introducing them to a new cluster of fans. It’s hard to know what those same newbies would have made of the album from which it came, though. Transmissions from the Satellite Heart is one the Flaming Lips’ best albums; it’s also one of their strangest and most ambitious, where throwaway ditties about girls who think of ghosts are scant but there’s plenty of sonic weirdness, from the pop-crunch of Turn It On to the dizzy heights of Oh, My Pregnant Head. Moth in the Incubator is a brilliantly trippy triptych that comes on like three songs cut-and-pasted together: it starts with a hazy acoustic strum, then it explodes into a nasty intergalactic jam with Coyne droning “I’ve been born before, I’m getting used to it,” like a reincarnated zombie, and finally finishes with a grand flourish of soaring noise, like magical sparks of sound whizzing overhead.

One of the Flaming Lips’ most charming songs, from 1995’s noise-pop spectacular Clouds Taste Metallic, with a premise so cosy and heartwarming it could be turned into a children’s picture book. It’s Christmas Eve, and a young Coyne decides to spread some Yuletide cheer to the local zoo by freeing all the animals. There’s just one snag: the critters don’t want his charity because, even though they’re miserable, they’d rather organise their own jailbreak and save themselves. “The elephants, orangutans / All the birds and kangaroos,” sings Coyne, over a sweet Beach Boys-like melody, underpinned by fuzzy, sludgy guitars and the sound of cymbals crashing like Christmas bells. “All said, ‘Thanks but no thanks, man / But to be concerned is good’.” In some parallel universe, listening to it every year on 24 December is as cherished a part of the Christmas ritual as watching The Snowman.

Guitarist Roland Jones quit the Lips a year after the release of Clouds Taste Metallic. When he left, he took the idea of a traditional, guitar-driven sound with him, leaving the rest of the band to find a new purpose. Their solution was Zaireeka. Inspired by the band’s old Parking Lot Experiments, in which Coyne had fans blast 40-odd cassette tapes from their car stereos at different times to create one long, perfectly-synced symphony, it’s one of the grandest follies ever: a single album split over four separate CDs, designed to be played simultaneously on four separate stereo systems. NME hailed it as a “work of genius” in its 10/10 review; it’s also still just one of a handful of albums to get a 0.0 score from Pitchfork. Look past the outlandish concept and you can find the first roots of the new Flaming Lips beginning to take shape, largely thanks to drummer Steven Drozd slowly shifting into the role of multi-instrumentalist. Thirty-Five Thousand Feet of Despair, for example, is still fantastic: a majestic mixture of throbbing strings, trembling piano and the terrifying roar of a jet engine as Coyne laments a pilot who’s “gone insane” and hangs himself in a bathroom mid-flight.

The Soft Bulletin, released in 1999, still stands as a pinnacle of what pop music can be at its most magical and inventive, an album rattling with wondrous sounds and ideas you’ll want to hold on to forever. On one hand, it’s their most sonically breathtaking work, built on otherworldly noises and instrumentation that sound as if they’re being beamed from a future disco in an orbiting space-station; on the other, it’s their most moving and vulnerable, too, with Coyne finding more frailty than ever before in his outlandish ideas. Race for the Prize, a touching tale of two scientists prepared to sacrifice themselves and find a cure that will save the world, is a belter: just listen, now, to the giant crack of those distorted drums, that giddy piano riff, the rush of those shrieking synthesised strings that fizz in your synapses like sherbert being poured on your brain. And then Coyne, somehow, touches looks past the HG Wells-like set-up to hit just the right nerve and bring you back down to Earth. “Theirs is to win / If it kills them,” he yelps. “They’re just humans with wives and children.” It’s four-odd minutes of glorious, perfect psych-pop, and a bittersweet sci-fi masterwork to boot.

The Soft Bulletin has so many special moments it could easily half-fill a 10 of the Best on its own. But on an album where nearly every song’s a gem, from the brittle beauty of The Spiderbite Song to The Spark That Bled’s gorgeous six-minute symphony, Feeling Yourself Disintegrate feels particularly precious. Here, Coyne floats high above the everyday muck and, cushioned by soft pillows of celestial synths and strings, realising that his body’s been slowly breaking apart ever since he was born; that all life is destined to die. “Love in our life is just too valuable / Oh to feel for even a second without it / But life without death is just impossible / Oh, to realise something is ending within us,” he sings gently, and for just a fleeting second, he’s grabbed hold of nirvana. In slightly grubbier fashion, The Soft Bulletin helped Warners see the light, too: after years of bemoaning the band’s lack of commercial success, they suddenly had a mainstream breakthrough act on their books. Their next project would be even bigger.

By 2002, The Flaming Lips weren’t cult weirdos anymore. If The Soft Bulletin had ended their status as beloved indie fuck-ups by turning them into a mainstream band, then Yoshimi Battles the Pink Robots helped establish them as a legitimate big deal. As ever, strangeness abounds, and the album’s quasi-concept gives a sci-fi bent to plenty of the songs: the first instalment of the two-part title track is bubblegum sci-fi, a catchy-as-hell ode to a young Japanese girl who brings down some killer androids; elsewhere, One More Robot/Sympathy 3000-21 finds those same machines developing pangs of human emotions, like a trippier take on Isaac Asimov’s short story I, Robot. But, as with The Soft Bulletin, there’s a real heart to Coyne’s lyrics that stops it from ever feeling too trivial. Fight Test takes the the melody of Cat Stevens’ weepy Father and Son but, courtesy of some splendid squelchy synths and lovely acoustic guitar, turns it into a meditation on self-respect and standing up for what’s right, as Coyne regrets not duffing up his ex’s new beau. “For to lose I could accept,” he sings. “But to surrender? I just wept and regretted this moment.” The prettiest space-rock endorsement of throwing down fisticuffs you’ll ever hear.

It’s previously been said that Do You Realize?? is quite similar to John Lennon’s Imagine, which in turn is like saying a T rex is a bit like a chicken: they might share some DNA, but that’s about it. Because while Imagine clucks around in its coop preaching soppy sanctimony over a hum-drum piano, Do You Realize?? is tilting back its big, beastly head and roaring magnificently at the sky above. It’s an anthem for the atheist generation: there’s no afterlife and we’re all going to be food for the worms eventually, but that doesn’t stop any of this from being beautiful. “Do you realize that everyone you know, someday, will die?” asks a wide-eyed Coyne, like a man who’s just clocked what carpe diem really means after chugging down some hallucinogens, and then suddenly there’s a giant wave of woozy noise that’s engulfing him and everything else, as bells chime and strings soar, and an angelic choir materialises out of thin air. Coyne has since described it as one of his proudest creations, stating: “A part of you makes it and you don’t really think that much of it. Then someone comes up and says ‘We used that song at my mother’s funeral.’ You can say it’s just a dumb song, or you can say, ‘I understand.’”

What’s really strange about last year’s Miley Cyrus & Her Dead Petz experiment, a 23-track album of wafty psych on which Coyne served as co-writer and co-producer, is just how drearily banal it is: there are songs about lactating nipples (Milky Milk Milk) and odes to smoking weed (Dooo It!), but it all sounds so safe. There have been other spots over the past 10 years, too, when the Lips have felt in danger of turning from fearless freaks into cuddly crusties; a group who have grown wacky in such a predictable, mild-mannered way you half-expect to see Coyne onstage sipping from a “You don’t have to be mad to work here, but it helps!” mug. But you doubt their capacity to still make something thrilling at your peril. 2009’s Embryonic is the Flaming Lips at their darkest and most dangerous: an album of evil noise and terrifying visions. Even the pop singles are odd: on I Can Be a Frog, Yeah Yeah Yeahs singer Karen O ribbits, growls and meows her way through a series of creepy animal impressions that’ll stop you from sleeping. She’s also one of the angry mob on the eerie din of Watching the Planets, on which Coyne makes like a cult leader waiting for the rapture. “Oh oh oh, burning the Bible tonight!” he chants manically, backed by spooky piano and pounding war-drums, as he spurs his followers on in some demented Wicker Man-like ritual. A nightmarish reminder that you should never get too close to The Flaming Lips; even if they’re tamer than they once were, they’ve still got teeth.